Geodesic
Critical groups of graphs with reflective symmetry
Journal of Algebraic Combinatorics, Tome 39 (2014) no. 1, pp. 209-224.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

The critical group of a graph is a finite Abelian group whose order is the number of spanning forests of the graph. For a graph $G$ with a certain reflective symmetry, we generalize a result of Ciucu-Yan-Zhang factorizing the spanning tree number of $G$ by interpreting this as a result about the critical group of $G$. Our result takes the form of an exact sequence, and explicit connections to bicycle spaces are made.
Classification : 05C25, 05C10, 05C62
Keywords: critical group, graph Laplacian, spanning trees, graph involution, bicycle space, involution 
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     author = {Berget, Andrew},
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     url = {http://geodesic.mathdoc.fr/item/JAC_2014__39_1_a0/}
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Berget, Andrew. Critical groups of graphs with reflective symmetry. Journal of Algebraic Combinatorics, Tome 39 (2014) no. 1, pp. 209-224. http://geodesic.mathdoc.fr/item/JAC_2014__39_1_a0/